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Publications Influence

The Riemann¿Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]

- A.B.J. Kuijlaars, K. McLaughlin, W. V. Assche, M. Vanlessen
- Mathematics
- 23 November 2001

Abstract We consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1− x ) α (1+ x ) β h ( x ), with α , β >−1 and h real analytic and strictly positive on… Expand

203 24- PDF

The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence Coefficients

- A. B. J. Kuijlaars, W. V. Assche
- Mathematics
- 1 July 1999

We study the zeros of orthogonal polynomials pn, N, n=0, 1, ?, that are generated by recurrence coefficients an, N and bn, N depending on a parameter N. Assuming that the recurrence coefficients… Expand

124 16- PDF

ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS VIA A POLYNOMIAL MAPPING

- J. Geronimo, W. V. Assche
- Mathematics
- 1 February 1988

Starting from a sequence {pn{x; no)} of orthogonal polynomials with an orthogonality measure yurj supported on Eo C (—1,1), we construct a new sequence {p"(x;fi)} of orthogonal polynomials on£ =… Expand

128 16- PDF

Orthogonal matrix polynomials and higher-order recurrence relations

- A. Dur'an, W. V. Assche
- Mathematics
- 5 October 1993

Abstract It is well known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation… Expand

162 13- PDF

Asymptotics for Orthogonal Polynomials

- W. V. Assche
- Mathematics
- 1 October 1987

Orthogonal polynomials on a compact set.- Asymptotically periodic recurrence coefficients.- Probabilistic proofs of asymptotic formulas.- Orthogonal polynomials on unbounded sets.- Zero distribution… Expand

178 11

Some classical multiple orthogonal polynomials

- W. V. Assche, E. Coussement
- Mathematics
- 15 January 2001

Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation… Expand

118 9- PDF

A random variable uniformly distributed between 2 independent random variables

- W. V. Assche
- Mathematics
- 1987

22 8

Orthogonal matrix polynomials and applications

- Ann Sinap, W. V. Assche
- Mathematics
- 31 January 1996

Orthogonal matrix polynomials, on the real line or on the unit circle, have properties which are natural generalizations of properties of scalar orthogonal polynomials, appropriately modified for the… Expand

100 6- PDF

Riemann-Hilbert Problems for Multiple Orthogonal Polynomials

- W. V. Assche, J. Geronimo, A. Kuijlaars
- Mathematics
- 2001

In the early nineties, Fokas, Its and Kitaev observed that there is a natural Riemann-Hilbert problem (for 2 x×2 matrix functions) associated with a system of orthogonal polynomials. This… Expand

127 5

Perturbation of Orthogonal Polynomials on an Arc of the Unit Circle, II

- L. Golinskii, P. Nevai, W. V. Assche
- Mathematics
- 8 October 1995

Orthogonal polynomials on the unit circle are fully determined by their reflection coefficients through the Szego? recurrences. Assuming that the reflection coefficients converge to a complex… Expand

53 5- PDF